Readers versed in computational persistence may observe that Algorithm  is essentially the cohomology algorithm, a standard method to compute persistent relative cohomology [1]}. Up to relabeling, this method amounts to an application of the “standard algorithm” [2]} to the antitranspose of \(D\) .
The procedure is “left-looking,” in the sense that no information about row \(i\)  of \(D\)  is needed until we construct row \(i\)  of \(  {R} ^{-1} \) .
